SECOND AMENDMENT TO SECURITIES PURCHASE AGREEMENT

Exhibit 2.40B

SECOND AMENDMENT TO SECURITIES PURCHASE AGREEMENT

This amendment (the “Second Amendment”) to that certain SECURITIES PURCHASE AGREEMENT, dated October 6, 2005 (the “Agreement”), as amended by the amendment on December 9, 2005 (the “Amendment”), is entered into by and among Comverse, Inc., a Delaware corporation (“Purchaser”), CSG Software, Inc., a Delaware corporation (“CSG Software”), CSG Americas Holdings, Inc., a Delaware corporation (“CSG Holdings”), CSG Netherlands BV, a company organized under the laws of the Netherlands (“CSG Netherlands”) and CSG Technology Limited, a company organized under the laws of Bermuda (“CSG Technology” and, together with CSG Software, CSG Holdings and CSG Netherlands, the “Companies”), CSG Systems International, Inc., a Delaware corporation (“CSG”), and CSG Netherlands CV, a partnership with limited liability organized under the laws of The Netherlands (“CSG Netherlands CV” and, together with CSG, the “Sellers”), with CSG Netherlands CV acting through its general partner, CSG International Holdings, LLC, a Delaware limited liability company (“CSG International”). Capitalized terms used but not defined herein shall have the meaning ascribed to such term in the Agreement.

WHEREAS, Purchaser, the Sellers and the Companies are all parties to the Agreement and the Amendment;

WHEREAS, Purchaser, the Sellers and the Companies wish to amend the Agreement and the Amendment as provided herein; and

WHEREAS, pursuant to Section 11.4 of the Agreement, all amendments to or waivers of any provision of the Agreement may be made by a written instrument signed by the parties thereto.

NOW, THEREFORE, for good and valuable consideration, the receipt, adequacy and sufficiency of which are hereby acknowledged, the parties hereto, intending to be legally bound, covenant and agree as follows:

1. Purchase Price Adjustment. The parties agree that the Closing Net Assets Statement, the Closing Working Capital Statement and the Closing Cash Statement set forth on Exhibit A hereto shall each be conclusive and binding upon the parties for purposes of the Agreement. The parties further agree that, in satisfaction of the obligations of Purchaser under Section 2.5(d), (i) Purchaser shall pay Seller three million seven hundred and ninety-six thousand dollars ($3,796,000) on or before February 17, 2006 (and, notwithstanding anything to the contrary contained in Section 2.5(d), without any interest thereon), and (ii) all amounts in the Escrow Account shall be released to Purchaser.

2. This Second Amendment shall serve as direction to the Escrow Agent from Sellers and Purchaser that, pursuant to Paragraph four (4) of the Escrow Agreement, the Escrow Agent shall distribute the Escrow Funds to Purchaser no later than five (5) days after receipt of this Second Amendment.

3. All references in the Agreement to “this Agreement,” and to all other words referring to the Agreement (such as “herein,” “hereto,” “herewith” and “hereunder”), shall be deemed to mean and refer to the Agreement, as amended by the Amendment and this Second Amendment. This Second Amendment and the rights and obligations of the parties under this Second Amendment shall be governed by, and construed and interpreted in accordance with, and the parties hereto agree to submit to the exclusive jurisdiction, of the state of New York, in connection with any action, suit or proceeding based on or arising under this Amendment. This Second Amendment may be executed in one or more counterparts, all of which constitute one and the same instrument. Each provision of this Second Amendment will be considered severable and if for any reason any provision which is not essential to the

effectuation of the basic purposes of this Second Amendment is determined by a court competent jurisdiction to be invalid or unenforceable and contrary to existing or future applicable law, such invalidity will not impair the operation of or affect those provisions of this Second Amendment which are valid. In that case, this Second Amendment will be construed so as to limit any term or provision so as to make it enforceable or valid within the requirements of any applicable law, and in the event such term or provision cannot be limited, this Second Amendment will be construed to omit such invalid or unenforceable provisions. The Agreement, as amended by the Amendment and this Second Amendment and by that certain side letter between Comverse and CSG with respect to the allocation of the Purchase Price, sets forth the entire understanding of the parties thereto with respect to all matters contemplated thereby and hereby and supersedes all previous agreements and understandings among them concerning such matters. No statements or agreements, oral or written, made prior to or at the signing hereof, shall vary, waive or modify the written terms hereof.

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IN WITNESS WHEREOF, the parties hereto have caused this Second Amendment to be signed on the date and year first above written.

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Exhibit A

Closing Net Assets and Working Capital Statements

(in thousands)

A-1

Closing Cash Statement

(in thousands)

A-2